Also note that Air NZ operates a joint venture with UAL on top of all the typical Star Alliance code-shares.

I would be interested to know if the LHR route is included in the JV.

Not that I can see. I checked 21 Feb LAX-LHR. ANZ 002 departs at 410P.
United only has one nonstop listed UA923 departing at 530P. If it were a codeshare, the Air New Zealand flight would have a UA number assigned to it and be bookable on United.com.